Answer
There would be only 3 spectral lines.
Work Step by Step
These were the six possibilities before, listed by initial and final quantum levels:
4 to 3
4 to 2
4 to 1
3 to 2
3 to 1
2 to 1
Here is the modified list when the energy levels are spaced equally from adjacent ones. There are just 3 distinct spectral lines.
4 to 3 = 3 to 2 = 2 to 1
4 to 2 = 3 to 1
4 to 1
The transition from 4 to 3 has the same difference in energy as that from 3 to 2 and from 2 to 1. So, the emitted photons all have the same energy, and there is just one spectral line.
Similarly, the transition from 4 to 2 has the same energy change as a transition from 3 to 1.
